We characterize the convex-cyclic weighted composition operators \(W_{(u,\psi )}\) and their adjoints on the Fock space in terms of the derivative powers of \( \psi \) and the location of the eigenvalues of the operators on the complex plane. Such a description is also equivalent to identifying the operators or their adjoints for which their invariant closed convex sets are all invariant subspaces. We further show that the space supports no supercyclic weighted composition operators with respect to the pointwise convergence topology and, hence, with the weak and strong topologies, and answers a question raised by T. Carrol and C. Gilmore in [5].

我们根据\( \psi \)的导数幂和特征值的位置来表征Fock 空间上的凸循环加权合成算子\(W_{(u,\psi )}\)及其伴随物。复平面上的算子。这样的描述也等价于确定它们的不变闭凸集都是不变子空间的算子或其伴随物。我们进一步表明，空间不支持关于逐点收敛拓扑的超循环加权组合算子，因此，弱拓扑和强拓扑，并回答了 T. Carrol 和 C. Gilmore 在 [5] 中提出的问题。